Question: Determine the intercepts of the line. $ 2x+5y=-6$ $y$ -intercept: $\Big($
The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}2\cdot{0}+5y&=-6\\ 5y&=-6\\ y&=-1.2\end{aligned}$ So the $y$ -intercept is $\left(0,-1.2\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}2x+5\cdot{0}&=-6\\ 2x&=-6\\ x&=-3\end{aligned}$ So the $x$ -intercept is $\left(-3,0\right)$. In conclusion, The $y$ -intercept is $\left(0,-1.2\right)$. The $x$ -intercept is $\left(-3,0\right)$.